Three charges $Q$,$+q$,and $+q$ are placed at the vertices of a right-angled isosceles triangle as shown. The net electrostatic potential energy of the configuration is zero if $Q$ is equal to

The value of $a$ for which the system of equations $a^3x + (a + 1)^3y + (a + 2)^3z = 0$,$ax + (a + 1)y + (a + 2)z = 0$,$x + y + z = 0$ has a non-zero solution is

Equation of one of the tangents passing through $(2,8)$ to the hyperbola $5 x^2-y^2=5$ is

$A$ husband and wife have normal vision,but the fathers of both of them were colour blind. What is the probability of their first daughter being colour blind (in $\%$)?

Hydathodes are also called

The electrode potentials for $Cu^{2+}_{(aq)} + e^- \to Cu^{+}_{(aq)}$ and $Cu^{+}_{(aq)} + e^- \to Cu_{(s)}$ are $+0.15 \ V$ and $+0.50 \ V$ respectively. The value of $E^\circ$ for the reaction $Cu^{2+}_{(aq)} + 2e^- \to Cu_{(s)}$ will be ............ $V$.